Please help me solve this?

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  • 3 months ago

    Since 4 is a zero, f(x) is divisible by x - 4.

    .................3x^2-19x +6

    .....--------------------------

    x-4|3x^3-31x^2+82x-24

    ......3x^3-12x^2

    ......---------------

    ..............-19x^2+82x

    ..............-19x^2+76x

    ...............--------------

    .............................6x-24

    .............................6x-24

    .............................-------

    ...................................0

    3x^3 - 31x^2 + 8x - 24 = 0

    (x - 4)(3x^2 - 19x + 6) = 0

    (x - 4)(3x - 1)(x - 6) = 0

    x = 4 or x = 1/3 or x = 6

  • x = 4 is a root, so x - 4 = 0 is a factor

    (x - 4) * (ax^2 + bx + c) = 3x^3 - 31x^2 + 82x - 24

    ax^3 + bx^2 + cx - 4ax^2 - 4bx - 4c = 3x^3 - 31x^2 + 82x - 24

    ax^3 = 3x^3

    a = 3

    bx^2 - 4ax^2 = -31x^2

    b - 4a = -31

    b - 12 = -31

    b = -19

    cx - 4bx = 82

    c - 4b = 82

    c + 76 = 82

    c = 6

    -4c = -24

    -24 = -24

    (x - 4) * (3x^2 - 19x + 6) = 3x^3 - 31x^2 + 82x - 24

    3x^2 - 19x + 6 = 0

    x = (19 +/- sqrt(361 - 72)) / 6

    x = (19 +/- sqrt(289)) / 6

    x = (19 +/- 17) / 6

    x = 2/6 , 36/6

    x = 1/3 , 6

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